Swarm Field Theory, Coherence Geometry and Unified Field Framework
Published September 19, 2025 | Version v1
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UFEB: A Simplified Update-Based Formulation of the Unified Field Equation

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Description

Description:
This paper presents the UFEB (Unified Field Equation, Budget form), a simplification of the Unified Field Equation in which explicit time is eliminated and all physical laws are expressed as discrete updates. Numeric demonstrations confirm that UFEB reproduces:

  • Relativistic update budgets (muon lifetime)

  • Electromagnetic constant closure (Z₀ → μ₀, ε₀)

  • Quantum per-update phases (particle-in-a-box, oscillator)

  • Conservation laws via discrete Noether invariance

  • Gravitational redshift expressed as a τ-ratio

UFEB functions as both a computational simplification and a conceptual reframing, showing that physics can operate fully without explicit time.

Additional materials and related work are available on GitHub: https://github.com/crumpler4/Swarm-Theory-Unified-Field-Equation-Series

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References

  • Einstein, A. (1905). Zur Elektrodynamik bewegter Körper. Annalen der Physik, 322(10), 891–921. https://doi.org/10.1002/andp.19053221004– Special relativity; source of Lorentz transformations.
  • Einstein, A. (1916). Die Grundlage der allgemeinen Relativitätstheorie. Annalen der Physik, 354(7), 769–822. https://doi.org/10.1002/andp.19163540702– General relativity; gravitational redshift foundation
  • Mohr, P. J., Newell, D. B., & Taylor, B. N. (2016). CODATA recommended values of the fundamental physical constants: 2014. Reviews of Modern Physics, 88(3), 035009. https://doi.org/10.1103/RevModPhys.88.035009– Authoritative source for μ₀, ε₀, Z₀, h, c, etc.
  • Tiesinga, E., Mohr, P. J., Newell, D. B., & Taylor, B. N. (2021). CODATA recommended values of the fundamental physical constants: 2018. Journal of Physical and Chemical Reference Data, 50(3), 033105. https://doi.org/10.1063/5.0064855– Latest CODATA update.
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  • Chou, C. W., Hume, D. B., Rosenband, T., & Wineland, D. J. (2010). Optical Clocks and Relativity. Science, 329(5999), 1630–1633. https://doi.org/10.1126/science.1192720– Precision optical clock measurements of gravitational redshift.
  • Yee, K. S. (1966). Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media. IEEE Transactions on Antennas and Propagation, 14(3), 302–307. https://doi.org/10.1109/TAP.1966.1138693– The Yee algorithm, foundational to the UFEB simulation appendix.
  • Barbour, J. (1999). The End of Time: The Next Revolution in Physics. Oxford University Press. – Philosophical argument that time is not fundamental.
  • Rovelli, C. (2018). The Order of Time. Riverhead Books.– Relational and emergent perspectives on time.
  • This work is part of the Swarm Theory: Unified Field Equation Series. Supporting materials and repository: https://github.com/crumpler4/Swarm-Theory-Unified-Field-Equation-Series